Having f1 & f2 we would of course find f1, f2, f1+f2 and f2-f1. Now this of course is the simplest view. Now when you apply f1 and f2 to your cell, are you assuming this simple approach to f results or are you considering a superposition mode of operation?

With enough energy placed into the cell and we assume the non-linear mixing, would we not see a very large and somewhat high in energy content vast number of additional frequencies?